1

Magnetic properties of (Fe1−xMnx)2AlB2 and the impact

of substitution on the magnetocaloric effect

D. Potashnikov,1,2 E.N. Caspi, 3,4,5 A. Pesach, 3 S. Kota,4 M. Sokol,4,6 L.A. Hanner,4 M.W.

Barsoum,4 H.A. Evans,5 A. Eyal,1 A. Keren1 and O. Rivin3

August 2020

1 Faculty of Physics, Technion - Israeli Institute of Technology, Haifa 32000, Israel

2 Israel Atomic Energy Commission, P.O. Box 7061, Tel-Aviv 61070, Israel

3 Department of Physics, Nuclear Research Centre-Negev, P.O. Box 9001, Beer Sheva 84190, Israel

4 Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA

5 Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.

6 Department of Materials Science and Engineering, Tel Aviv University, Ramat Aviv 6997801, Israel

Abstract

In this work, we investigate the magnetic structures of (Fe1−xMnx)2AlB2 solid-solution

quaternaries in the x = 0 to 1 range using x-ray and neutron diffraction, magnetization

measurements, and mean-field theory calculations. While Fe2AlB2 and Mn2AlB2 are known to be

ferromagnetic (FM) and antiferromagnetic (AFM), respectively, herein we focused on the

magnetic structure of their solid solutions, which is not well understood. The FM ground state of

Fe2AlB2 becomes a canted AFM at x ≈ 0.2, with a monotonically diminishing FM component until

x ≈ 0.5. The FM transition temperature (TC) decreases linearly with increasing x. These changes in

magnetic moments and structures are reflected in anomalous expansions of the lattice parameters,

indicating a magnetoelastic coupling. Lastly, the magnetocaloric properties of the solid solutions

were explored. For x = 0.2 the isothermal entropy change is smaller by 30% than it is for Fe2AlB2,

while the relative cooling power is larger by 6%, due to broadening of the temperature range of

the transition.

I. Introduction

The discovery of a giant magnetocaloric effect (MCE) near room temperature (RT) in

Gd5(Si2Ge2)1 sparked an increasing interest in magnetic-based refrigeration. The numerous

advantages of magnetic-based refrigeration include the elimination of moving parts and harmful

gases. This method, known as active magnetic regeneration, is thus more efficient and

environmentally “greener” compared to the current gas compression technology.2 However, most

of the known materials exhibiting a giant MCE near RT contain Gd, or other rare earths, that are

too expensive for mass production. Therefore, research in the field has gravitated to magnetic

2

materials containing more abundant elements such as the transition metals (TM) with magnetic

ordering temperatures near RT. Examples include FeMnP1−xAsx3 and Mn1.25Fe0.70P1−xSx,

4 which

have tunable magnetic ordering temperatures and high magnetic entropy changes, and Ni-Mn-Sn

Heusler alloys, which show a giant inverse MCE.5

Recently, the TM borides with the chemical formula M2AlB2, where M = (Fe, Mn, Cr) have

attracted much interest.6,7 The compounds in this family (also called MAB phases) crystallize in

the orthorhombic Cmmm space group with slabs of M2B2 stacked in between Al layers along the

b axis. Magnetic studies on the MAB phases have revealed that Fe2AlB2 orders ferromagnetically

(FM) below ≈300 K,8 Mn2AlB2 orders antiferromagnetically (AFM) below ≈313 K,9 and Cr2AlB2

is paramagnetic (PM).10 The near-RT FM phase transition of Fe2AlB2, along with it being

composed of entirely earth-abundant and nontoxic elements, renders it a potential candidate for

magnetic refrigeration. A large number of MCE studies in Fe2AlB2 are available (see Ref. 7 and

references therein), which measure an isothermal entropy change of ≈4 J/kg K and an adiabatic

temperature change of ≈2 K due to an applied field (H) of 2 T.

In an attempt to improve the available MC properties, several studies of MAB solid solutions,

on both the M and/or A sites, were carried out.11–16 For example, studies on the solid solution

(Fe1−xMnx)2AlB2 have shown that the addition of Mn gradually decreases the FM moments and

the FM transition temperature. At intermediate Mn concentrations, the magnetic structure is

hypothesized to be either a spin glass12 or a disordered ferrimagnet,13 due to competing magnetic

interactions, but it has yet to be directly observed. The addition of AFM interactions is also known

to widen the temperature range of the magnetic transition,17 and thus allow for additional control

over the MCE in the solid solution.

In order to further understand the magnetic properties of the (Fe1−xMnx)2AlB2 system and

enable fine tuning of its magnetic properties, we investigated the magnetic phase diagram of this

system using x-ray, neutron diffraction and magnetization measurements. The measurements are

qualitatively explained by a mean-field calculation of the magnetic phase diagram in the x–T plane.

II. Experimental Details

A. Sample preparation and characterization

All compositions were prepared via a two-step reactive powder metallurgy route in a horizontal

alumina tube furnace under flowing argon, Ar, as described in detail in the Supplemental Material

(SM).18 Samples with 11B (Cambridge Isotopes, 98%) were made with nominal Mn concentrations

of x = 0, 0.05, 0.1, 0.2, 0.25, 0.5, and 1. Additionally, samples with natural B were made with

nominal Mn concentrations of x = 0.2, 0.3, 0.5, 0.75, and 1.

X-ray powder diffraction (XRD) of (Fe1−xMnx)2Al11B2 (x = 0, 0.05, 0.1, 0.2, 0.25, 0.5, 1) was

performed using a Rigaku SmartLab diffractometer, equipped with a Cu K radiation source and

detector-side graphite monochromator. Additional samples with natural B (x = 0.5, 0.75 and 1)

were also measured. A step size of 0.015o and 6–8 s of dwell time per step was used in all cases.

3

The samples with x = 0.5 and 0.75 were also measured using the low background Bruker D8-

Advance diffractometer, using CuKα radiation and an angular range of 10°–100° in steps of 0.01°.

B. Magnetic properties

Magnetization measurements were performed using a Quantum Design MPMS3 system at the

Quantum Material Research center in the Technion. Zero-field-cooled (ZFC) and field-cooled

(FC) temperature scans were performed under a magnetic field (H) of 50 Oe (μ0 Oe = 10−4 Tesla).

Field scans at constant temperatures were also carried out using H in the 0–70 kOe range.

C. Neutron powder diffraction

Three of the samples containing the 11B powders with x = 0, 0.1, and 0.2 were measured in the

temperature ranges of 8–350 K (x = 0) and 8–300 K (x = 0.1, 0.2) using the BT-1 diffractometer

at the National Center for Neutron Research located at the National Institute for Standards and

Technology, USA. An incident wavelength of 2.079 Å was obtained using the Ge(311)

monochromator and an in-pile collimation of 60’. The samples were loaded into a vanadium holder

with a diameter of 9.2 mm. Two additional powders with x = 0.25 and 0.5, were measured using

the KANDI-II diffractometer at the Israel Research Reactor II located at the Nuclear Research

Center Negev, Israel.19 The x = 0.5 sample was measured at 3, 100, 200, and 298 K, while the x =

0.25 sample was measured at 3 and 298 K.

III. Theory

The magnetic properties of the (Fe1−xMnx)2AlB2 system were modelled in the framework of

the mean field theory (MFT) as described in Ref. 20. As noted above, the M2AlB2 unit cell has the

orthorhombic Cmmm symmetry, where the M, Al and B atoms occupy the 4j, 2a, and 4i sites,

respectively [Fig. 1(a)]. The magnetic ground states of the end compounds were previously

determined by neutron diffraction to be FM for Fe2AlB2 [Fig. 1(b)] and AFM for Mn2AlB2 [Fig.

1(c)].8,21 In the former case the magnetic moments are oriented along the crystallographic a axis.

In the latter case, the magnetic unit cell is twice the size of the chemical unit cell along the c axis

[propagation vector k = (0, 0, 1/2)].21 The four magnetic moments in the chemical unit cell are all

parallel and point along the crystallographic b axis.9

The reported possibility for low-dimensional magnetism9 and canting of the Mn moments21

in Mn2AlB2 was not taken into account in the present study. As discussed in the next sections, the

estimated canted FM moment of ~8 ×10−3 μB21 is two orders of magnitude below the detection

limit of the neutron powder diffraction (NPD), and therefore cannot be observed by this method.

Mn2AlB2 shall therefore be treated as a simple AFM. Since the four moments in the chemical unit

cell are all parallel and equivalent in the magnetic ground states of the end compounds, a simplified

description of the M2AlB2 compounds is obtained by averaging the four magnetic moments in the

chemical unit cell into a single super moment. This simplifies the magnetic sublattice into a

primitive orthorhombic Bravais lattice. Furthermore, in the zeroth approximation of the MFT,22,23

the nearest neighbors along different crystallographic axes cannot be distinguished. The relative

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magnitudes of the exchange constants Jij along the a, b, and c crystal axes are then taken to be

equal [cubic lattice approximation, Fig. 1(d)].

To allow the description of an AFM unit cell, the cubic lattice is split into two sublattices

(A and B) along the c axis [Fig. 1(d)]. The crystal directions are denoted using α and β. The single

site Hamiltonian is then given by

��Fe,𝐴 = −{∑𝑧(𝑐𝐴𝐴) [(1 − 𝑥)𝐽Fe−Fe(𝑐𝐴𝐴),𝛼𝛽 ⟨��Fe,𝐴

𝛽 ⟩ + 𝑥𝐽Fe−Mn(𝑐𝐴𝐴),𝛼𝛽 ⟨��Mn,𝐴

𝛽 ⟩]

𝑐𝐴𝐴

+∑𝑧(𝑐𝐴𝐵) [(1 − 𝑥)𝐽Fe−Fe(𝑐𝐴𝐵),𝛼𝛽 ⟨��Fe,𝐵

𝛽 ⟩ + 𝑥𝐽Fe−Mn(𝑐𝐴𝐵),𝛼𝛽 ⟨��Mn,𝐵

𝛽 ⟩]

𝑐𝐴𝐵

+ 𝜇B𝑔Fe𝛼𝛽𝐻𝛽} ��Fe,𝐴

𝛼

= −𝐴Fe𝛼 ��Fe,𝐴

𝛼 ,

(1)

where cAA denotes the intrasublattice coordination shells, cAB denotes the intersublattice

coordination shells, z(c) is the coordination number of the cth shell, x is the Mn occupancy, JM-M'(c),αβ

are the anisotropic exchange constants of the cth coordination shell between M and M’ atom types,

µB is the Bohr magneton, gM

αβ is the anisotropic magnetic g-factor of atom type M, H – is the applied

field, SM,Aα

is the spin operator of atom type M, on sub-lattice A, and ⟨ ⟩ denotes thermal

averaging. We split the first six nearest neighbors of the cubic lattice into two coordination shells:

4 atoms on sublattice A and 2 atoms on sublattice B [Fig. 1(d)].

FIG. 1. (a) The chemical unit cell of M2AlB2, (b) FM structure of Fe2AlB2,8 (c) AFM structure of

Mn2AlB2,21 and (d) sublattice structure of simplified mean-field model of M2AlB2.

5

The full Hamiltonian (per atom) of the system is obtained from the single-site Hamiltonians as

�� =1

2(1 − 𝑥)(��Fe,𝐴 + ��Fe,𝐵) +

1

2𝑥(��Mn,𝐴 + ��Mn,𝐵),

(2)

where HM,δ is the single-site Hamiltonian for atom type M on sub-lattice δ = A or B, and is obtained

by replacing Fe with Mn and A with B in Eq. (1). To find the magnetization of each atom we need

to solve the mean-field self-consistent equations:

⟨��𝑀,𝛿𝛼 ⟩ = Tr [��𝑀,𝛿

𝛼 e−(��𝑀,𝛿 𝑘B𝑇⁄ )

𝑍𝑀,𝛿] , 𝑍𝑀,𝛿 = Tr[e−(��𝑀,𝛿/𝑘B𝑇)],

𝑀 = Fe,Mn𝛿 = 𝐴, 𝐵

,

(3)

where T is the sample temperature and kB is Boltzmann’s constant. Equation (3) can be expressed

as

⟨��𝑀,𝛿𝛼 ⟩ = 𝑆𝑀B𝑆𝑀 (

|𝛅𝑀|𝑆𝑀𝑘𝐵𝑇

)δ𝑀𝛼

|𝛅𝑀|

B𝑆(𝑥) ≡2𝑆 + 1

2𝑆coth (

2𝑆 + 1

2𝑆𝑥) −

1

2𝑆coth (

𝑥

2𝑆)

(4)

where δM is the mean field of atom M on sublattice δ, as defined in Eq. (1). The on-site

magnetization is then obtained from

𝑀𝛼(𝑇, 𝑥, 𝐻𝛽) = 𝜇B(𝑔Fe𝛼𝛽(1 − 𝑥)⟨��Fe,𝐴

𝛽 ⟩ + 𝑔Mn𝛼𝛽𝑥⟨��Mn,𝐴

𝛽 ⟩).

(5)

The critical temperature is obtained by numerically finding the temperature at which the on-site

magnetization vanishes.

IV. Results and analysis

A. X-ray powder diffraction

The XRD patterns of (Fe1−xMnx)2AlB2 powders at RT as a function of x are shown in Fig.

2. The reflections are consistent with an orthorhombic phase having the symmetry group Cmmm

and lattice parameters (LPs) a ≈ 2.9, b ≈ 11 and c ≈ 2.9 Å. Additional reflections belonging to

impurity phases are present in small amounts (≈5%) for all samples, except x = 0.5. In the x = 0.5

sample, the 11B powder was contaminated with SiO2, and thus a relatively large amount of

impurities is present. Some of the impurity reflections were identified to belong to Al2O3 (R-3c) 24

and Fe4Al13 (C2/m).25 The XRD patterns were refined using Rietveld refinement as implemented

in the FULLPROF package.26

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Table I. Refined LPs, unit-cell volume (V), nominal and refined Mn occupancy (x), Debye-Waller

factor (B) and weight percent of (Fe1−xMnx)2AlB2 phase at room temperature obtained by XRD

and NPD. The numbers in parentheses are the standard uncertainties from the Rietveld refinement

procedure. A systematic error of 0.03% is estimated between the NPD and XRD LPs and is

discussed in Sec. IV C.

Method Nominal

x

Refined

x a (Å) b (Å) c (Å) V (Å3) B (Å2) Wt.%

XRD 0a,c N/A 2.9261(1) 11.0316(4) 2.8677(1) 92.568(5) --- 99(1)

0.05a,c N/A 2.9267(1) 11.0248(4) 2.8696(1) 92.589(6) --- 98(3)

0.1a,c N/A 2.9281(1) 11.0269(4) 2.8774(1) 92.905(5) --- 97(2)

0.2a,c N/A 2.9297(1) 11.0239(4) 2.8842(1) 93.150(6) --- 98(2)

0.25a,c N/A 2.92922(4) 11.0203(2) 2.88702(4) 93.195(2) --- 97.4(7)

0.5b,c N/A 2.9264(1) 11.0139(3) 2.9004(1) 93.481(5) --- 96(2)

0.5b,d N/A 2.92892(8) 11.0250(3) 2.90452(7) 93.791(4) --- 87.9(6)

0.75b,c N/A 2.9263(2) 11.0372(5) 2.8998(2) 93.657(8) --- 81(2)

0.75b,d N/A 2.92733(5) 11.0446(2) 2.90188(5) 93.821(3) --- 85.1(4)

1a,c N/A 2.92025(7) 11.0613(3) 2.89568(7) 93.536(4) --- 97(2)

1a,21 N/A 2.92267(3) 11.0715(1) 2.89776(3) 93.767(2) --- 68.3(5)

NPD 0a,e 0 2.92526(2) 11.0330(1) 2.86767(3) 92.552(1) 0.06(4) 99(1)

0.1a,e 0.096(4) 2.92746(3) 11.0287(1) 2.87765(3) 92.908(2) 0.35(3) 99(1)

0.2a,e 0.190(2) 2.92850(4) 11.0237(2) 2.88489(4) 93.132(2) 0.42(3) 99(1)

0.25a,f 0.228(4) 2.9290(3) 11.019(1) 2.8876(3) 93.19(2) 0.44(4) 98(1)

0.5a,f 0.461(3) 2.9328(2) 11.029(1) 2.9062(2) 94.00(1) 0.44g 59(1)

1a,21 1 2.9166(6) 11.048(3) 2.8930(6) 93.22(4) 1.1(1) 100 a 11B sample b Natural boron sample c Measured using a Rigaku X-ray diffractometer d Measured using a Bruker X-ray diffractometer e Measured using the BT-1 neutron diffractometer f Measured using the KANDI-II neutron diffractometer g Fixed using the value for x = 0.25 to avoid divergence.

7

FIG. 2. Observed XRD patterns (symbols) and the corresponding Rietveld refinement (solid lines)

for different (Fe1−xMnx)2AlB2 powders with various x values. Reflections are labeled by their

Miller indices; impurity reflections are marked by * for α-Al2O3 and # for (Fe1-yMny)4Al13. The

patterns for x = 0.5 and 0.75 were measured on a natural B sample. All patterns shown here were

obtained using a Rigaku diffractometer.

The refined profile consisted of the main orthorhombic phase as well as α-Al2O3 for all

samples. The (Fe1-yMny)4Al13 reflections were found in the x = 0.5 and 0.75 samples with natural

B (Figures S1 and S2 in the SM) and added to the refined profile. The refined parameters for the

main phase were the LPs (Table I) and the atomic y positions at the 4j and 4i sites. The overall

Debye-Waller factor could not be refined due to the limited Q range of the diffractometer.

Additional reflections present at Q ≈ 2.33 and 2.52 Å−1 (for x = 0.1 and 0.2) and Q ≈ 2.7 Å−1 (for

x = 1) were not found to belong to any phase containing Fe, Mn, Al, B or any of their oxides.

The obtained LPs (Table I, Fig. 3) vary nonlinearly and nonmonotonically with x, and

deviate considerably from Vegard’s law.27 The unit-cell volume expands from ≈92.5 Å3 for

Fe2AlB2 up to ≈93.5 Å3 for Mn2AlB2. These results agree with previous reports by Cedervall et

al.13 but are lower than those reported by Chai et al.11 The a and c LPs expand before contracting,

while the b LP contracts before expanding. The transition point in all cases is for x in the range

0.2–0.5. The deviation of the LPs from Vegard’s law for large x is attributed to magnetostriction

within the sample, since for x ≳ 0.5 the sample becomes AFM at RT, as will be shown in Sec. IV

C.

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FIG. 3. Refined LPs and unit-cell volumes of (Fe1−xMnx)2AlB2 powders at RT as function of x

obtained from XRD (black symbols) and NPD (red symbols). (a), (b), and (c) show the a, b, and c

LPs, respectively and (d) unit-cell volume. Circles indicate measurements performed on natural B

samples; squares indicate those performed on 11B samples. Samples measured with NPD are

plotted using the refined x. The discrepancies between the NPD and XRD measurements of the

same samples originate from systematic errors which are discussed in Sec. IV C.

B. Magnetization measurements

The temperature dependent magnetization curves (Fig. 4) show varying magnetic

responses for different x values. As temperature decreases, samples with x < 0.5 show an abrupt

increase in magnetization, as expected for a FM. For x = 0.5 the increase in magnetization is not

as abrupt, while for x = 0.75 and x = 1 the total magnetic moment is two orders of magnitude lower.

Extrema in the derivative of the magnetization (Fig. 5) are used to determine temperatures

of possible magnetic events and the large minima for samples with x < 0.5 are used to estimate the

critical temperature (TC) for the FM phase. As x increases, additional extrema appear in the

derivative [Fig. 5(a), inset]. The origin of these extrema is unclear. However, since the samples

with high Mn content also contained more impurity phases, it is possible that these extrema are

due to the latter.

The saturated average magnetic moment at 2 K (Table II) is obtained from the high field

magnetization [Fig. 6(a)] by linear extrapolation of M as function of 1/H curves to H = 0 (not

shown). The number of data points to include in the linear fit was reduced until the sum of squared

residuals (χ2) did not change. The field-dependent measurement performed at temperatures below

and above TC are used to give a better estimate of TC by using an Arrott plot (Fig. S3 in the SM)

9

as described in Ref. 28.18 The new estimates for TC (Table II) show a systematic increase of ≈4%

compared to estimates obtained from dM/dT (not shown).

To estimate the magnetocaloric properties of the sample, the isothermal entropy change

[Table II, Fig. 6(b)] is calculated by numerically integrating the Maxwell relation:

𝛥𝑆𝑚(𝑇, 𝐻) = ∫ (𝜕𝑀

𝜕𝑇)𝐻′𝑑𝐻′

𝐻

0

≈ ∑𝑀𝑖 −𝑀𝑖−1

𝑇𝑖 − 𝑇𝑖−1(𝐻𝑖 −𝐻𝑖−1)

𝑛−1

𝑖=0

(6)

The maximum relative cooling power (RCP, Table II) is estimated by multiplying the maximal

value of ΔSm by the full width at half maximum (FWHM) of the measured ΔSm curve as a function

of T [Fig. 6(b)].29 The calculated RCP of Fe2AlB2 for a field change of 0‒2 T and 0‒5 T are 75

and 210 J/kg, respectively. These values are in agreement with results obtained in the literature.30,31

FIG. 4. ZFC magnetization for (a) x ≤ 0.5, and (b) x > 0.5. Measurements for x = 0.3, 0.5, and 0.75

were performed on natural B samples. Error bars are smaller than line widths. Note: emu/(g Oe) =

4π × 10−3 m3/kg.

10

FIG. 5. Derivatives of the ZFC magnetization for (a) x ≤ 0.5 and (b) x > 0.5. Inset in (a) shows a

zoomed-in view of the low-temperature regions. Measurements for x = 0.3, 0.5, and 0.75 were

performed on natural B samples. Note: emu/(g Oe) = 4π × 10−3 m3/kg.

11

FIG. 6. (a) Field-dependent average magnetic moment of (Fe1−xMnx)2AlB2 at 2 K as function of x.

(b) Isothermal magnetic entropy change for a field change of 0–20 kOe as function of the relative

temperature. Measurements for x = 0.3, 0.5, and 0.75 were performed on natural B samples. The

standard errors are smaller than the symbol size. Note: μ0 Oe = 10−4 Tesla.

C. Neutron powder diffraction

The majority of observed reflections in the NPD of all samples at the respective highest

measured temperature [cf. Fig. 7(a) for Fe2AlB2] are consistent with an orthorhombic (Cmmm)

phase having LPs a ≈ 2.9 Å, b ≈ 11 Å, and c ≈ 2.9 Å. Rietveld refinement of the observed NPD

patterns from this sample consisted of a single phase having an orthorhombic (Cmmm) symmetry

with the starting LPs mentioned above. The atomic y positions of the 4j and 4i sites, as well as the

overall Debye-Waller factor, were also refined. Instrumental resolution parameters, zero shift of

the detector angle (2θ) and the Mn occupancy in the 4j site were refined for the NPD data at the

highest measured temperature and then fixed for all subsequent refinements.

A similar analysis was performed for the other samples measured on BT-1. The

instrumental resolution of the KANDI-II diffractometer was determined using a Si standard and

was fixed for the refinement of the x = 0.25 and 0.5 samples. The refinement then consisted of the

same steps as for the BT-1 samples. In general, the refined RT LPs (Table I) are in agreement with

the LPs obtained from XRD, however some deviation, which is larger than the reported statistical

uncertainty, is observed. The NPD a LP is lower than that of the XRD LP by ≈0.03% for x = 0,

0.1, and 0.2 while the b and c LPs are overestimated by ≈0.02%.

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Table II. Transition temperatures (TC and TN), saturated average magnetic moment at 2 K (Msat),

magnetic entropy change (Sm), and relative cooling power (RCP). Ordered FM (µFM) and AFM

(µAFM) moments of (Fe1−xMnx)2AlB2 as determined by NPD at base temperature. Numbers in

brackets indicate uncertainty. The systematic error in Sm and RCP is expected to be on the order

of 10%.28

x TC (K)a TN (K)b Msat (μB) -Sm

(J/kg K)

2 T/5 T

RCP

(J/kg),

2 T/5 T

µFM (µB) µAFM (µB)

0c 292.4(2) --- 1.19(6) 2.7/5.7 75/210 1.30(4) 0

0.096(4)c 264.6(3) --- 1.18(6) 2.2/4.6 79/218 1.25(5) 0

0.190(2)c 231.4(3) 80 ± 20 1.12(6) 1.9/4.0 80/226 1.07(4) 0.24(4)

0.228(4)c 212.25(5) 150 ± 100 0.9(1) 1.4/2.9 70/190 0.97(6) 0.54(2)

0.30(2)d 183.16(6) --- 0.70(4) 0.7/1.4 41/117 --- ---

0.461(3)c --- 350 ± 50 --- --- --- 0 0.83(2)

0.50(5)d 130(5) --- 0.454(3) --- --- --- ---

121,c --- 3139 --- --- --- 0 0.71(2) a Critical temperature of the FM component as determined from Arrott plots. b Critical temperature of the AFM component as estimated from NPD measurements. The

uncertainties marked with ± indicate upper and lower bounds. c 11B sample d Natural B sample

Since these discrepancies show the same trend for three different samples, it is safe to

assume that they originate from a calibration discrepancy between the XRD and NPD

diffractometers. The deviation in the LPs at x = 0.5 is attributed to the poor sample quality, which

affects the refinement of the LPs due to the low resolution of the KANDI-II diffractometer, and

the deviation for x = 1 was found to originate from a systematic error in the calibration of the E6

diffractometer.21 In general, the Mn occupancy is in good agreement with the nominal

compositions of the samples, which shows that the (Fe1−xMnx)2AlB2 system is thermodynamically

stable over the whole Mn concentration range.

For Fe2AlB2, below 310 K, an increase in the intensity of the (001) reflection [Fig. 7(a),

inset] is observed, and is consistent with the onset of FM order, which was shown earlier (see Sec.

IV B). We therefore performed an additional refinement of the NPD data (for all temperatures)

which included a magnetic phase, with the Fe spins aligned along the crystallographic a axis.

Above 290 K, the fit agreement factor for the magnetic phase (Rmag) shows a large decrease in fit

quality, while a refined moment of 0.3 µB is obtained. We therefore take this value as the sensitivity

limit for a FM moment of the (Fe1−xMnx)2AlB2 system in the BT-1 diffractometer.

A similar analysis was performed for other compositions. A FM phase was added to all

refinements at T < 260 K for x = 0.1 (Fig. S4 in the SM) and at T < 220 K for x = 0.2. Below 100

K, an additional reflection appeared at Q ≈ 1.08 Å−1 [Fig. 7(b)] in the NPD data of the

(Fe0.8Mn0.2)2AlB2 sample. This reflection was identified to be the same AFM configuration found

13

in Mn2AlB2 (see Sec. II). The refinement therefore contained an AFM phase for all measurements

of (Fe0.8Mn0.2)2AlB2 with T < 100 K. The sensitivity limit of BT-1 for an AFM moment was

determined to be 0.2 μB in the same manner as for the FM moment. For the (Fe0.75Mn0.25)2AlB2

composition, the refinement at 3 K contained both an FM and AFM phases (Fig. S5 in the SM).18

The sensitivity limits of the KANDI-II diffractometer were determined by refining both magnetic

phases at RT for the x = 0.25 sample, and were found to be 0.4 μB and 0.2 μB for the FM and AFM

moments, respectively. The diffraction pattern of (Fe0.5Mn0.5)2AlB2 at RT showed an excess

neutron count at the position of the (0, 0, 1/2) reflection (Fig. S6 in the SM),18 which did not appear

in the XRD pattern, excluding the possibility for an impurity phase. An attempt to add a FM phase

to the refinement did not change the values for the refined parameters, showing no correlation

between the FM moment and other parameters. The FM moment of 0.45 μB, observed by

magnetization measurements (Table II) could not be detected by NPD for this sample. Therefore,

although both the FM and AFM phases are present, only the AFM phase was included in the

refinement for this sample.

FIG. 7. (a) Observed NPD pattern of Fe2AlB2 powders (symbols) at 350 K, the corresponding

Rietveld refinement (solid line) and their difference (blue bottom solid line). Inset zooms in on the

FM reflection at 8 K. (b) Observed NPD (symbols) of (Fe0.8Mn0.2)2AlB2 at different temperatures

and the corresponding Rietveld refinements (solid line). Reflections are marked using their Miller

indices and fractional Miller indices (for AFM reflections). Reflections marked by “?” correspond

to unidentified impurity phases. The measurements were performed using the BT-1 diffractometer.

The error bars are smaller than the symbol size.

14

The temperature evolution of the LPs for Fe2AlB2 [Fig. 8(a)] shows an expansion of the c LP upon

cooling below 310 K. Combined with the onset of FM ordering below this temperature, it is

reasonable to conclude that this anomalous thermal expansion most likely originates from

magnetostriction. These results agree with density-function theory (DFT) calculations by Ke et

al.,32 that have shown a strong dependence of the magnetic moment in Fe2AlB2 on the c LP. The

changes in the LPs over most of the x range are of the order of 0.25%. A similar behavior is

observed for the x = 0.1 and 0.2 samples (Fig. S7 in the SM),18 while an expansion of the b LP

upon cooling is observed for x = 1.21 For x = 0.5 [Fig. 8(b)], the c LP contracts below 200 K and

expands below 100 K. This change in behavior is attributed to the FM transition observed at ≈130

K (Table II).

FIG. 8. Temperature evolution of the a and c LPs (left y axis) and b (right y axis) of (a) Fe2AlB2

and (b) (Fe0.5Mn0.5)2AlB2 samples determined from NPD patterns.

V. Mean field theory analysis

The observed magnetic reflections (Fig. 7) indicate that the magnetic structure of

(Fe1−xMnx)2AlB2 is composed of two parts: a FM moment, which points along the crystallographic

a axis, and an AFM moment, which points along the crystallographic b axis with a propagation

vector of k = (0, 0, 1/2). The temperature evolution of each magnetic component [Fig. 9(a),

symbols] shows a gradual decrease, typical of a second-order phase transition. The FM and AFM

components, when present, have different critical temperatures and ground-state magnitudes, that

vary with x (Table II). The phase diagram of (Fe1−xMnx)2AlB2 [Fig. 9(b), symbols] thus consists

15

of three different phases. For x < 0.23, only a FM phase is present. For 0.23 < x ≤ 0.46, both FM

and AFM phases are present, while for 0.46 < x ≤ 1 only an AFM phase is present.

To investigate the magnetic moment dependence on x and T, we made use of Eq. (5). The

unknown parameters in the model are the g factors and spins of the Fe and Mn atoms, and the

exchange constants. Since the FM component is directed along the a axis, while the AFM

component is directed along the b axis, we only need to consider the exchange constants along

these directions. This leaves us with four exchange constants, namely: JFe-Fe(c),xx

, JFe-Mn(c),xx

, JFe-Mn(𝑐),yy

, and

JMn-Mn

(c),yy. We assume the g factors of the two atoms to be isotropic, i.e., g

I

αβ=g

I0δαβ

. The fitting

procedure is obtained as follows. The values of SFe and SMn are scanned in the range 0.5–3 in steps

of 1/2. For each pair (SFe, SMn) gFe and JFe-Fe(c),xx

are obtained by fitting the temperature evolution of

the ordered magnetic moment, μ(T) for Fe2AlB2; gMn and JMn-Mn

(c),yy are obtained by fitting μ(T) for

Mn2AlB2 [Fig. 9(a)]. Next, JFe-Mn(c),xx

and JFe-Mn(𝑐),yy

are fitted to best match μ(T) for x = 0.1, 0.2, 0.25, and

0.5 [Fig. 9(a), solid line]. The χ2 goodness of fit parameter is used to identify the best-matching

fit, while also requiring that the resulting values for the exchange parameters remain positive. The

entire fitting procedure was performed twice where JFe-Mn(c),xx

and JFe-Mn(𝑐),yy

were assumed to be FM or

AFM along the c axis. Finally, the best-matching parameters were obtained by calculating μ(x) at

base temperature (Fig. 10). The only parameter set which predicted the existence of a nonzero FM

moment for x = 0.5 was SFe = 3/2, SMn = 1/2, gFe = 0.86(2), and gMn = 1.38(1). The values for the

exchange constants (in meV) are JFe-Fe(c),xx

= 3.67(8), JFe-Mn(c),xx

= 2.3(5), JFe-Mn(𝑐),yy

= 11.7(4), and JMn-Mn

(c),yy =

18.9(2). The sign of JFe-Fe(c),xx

and JFe-Mn(c),xx

is positive along all directions, while the sign of JFe-Mn(𝑐),yy

and

JMn-Mn(𝑐),yy

is negative along the c axis.

16

FIG. 9. (a) Temperature evolution of observed total ordered magnetic moment (symbols) in

(Fe1−xMnx)2AlB2. (b) Observed (symbols) and calculated (solid lines) critical temperature of FM

(black) and AFM (red) components as function of x. Different regions in the phase diagram are

labeled by magnetic phases present in them.

17

FIG. 10. Observed ordered magnetic moments at base temperature as function of x. Solid lines are

fits of Eq. (5).

VI. Discussion

The calculated magnetic phase diagram of the solid solution (Fe1−xMnx)2AlB2 [Fig. 9(b)]

contains three types of ordered magnetic structures: a FM structure below a critical Mn

concentration of x1 ≈ 0.1, an AFM structure above x2 ≈ 0.5, and a combination of both in between.

This intermediate region is interpreted as a canted AFM. Because the LPs of Fe2AlB2 and Mn2AlB2

differ significantly (Table I), a separation of the sample into Fe-rich and Mn-rich clusters would

produce two distinctly visible diffraction patterns. Since only a single diffraction pattern is

observed, with no broadening of the crystallographic or magnetic reflections relative to the

instrumental resolution, we conclude that the mixing of Mn in the sample is homogeneous and that

the observed combination of FM and AFM structures is to be interpreted as a canting of the FM

moments. The canting angles, in the a-b plane relative to the b-axis, at base temperature are

estimated to be 13(2) ° and 29(2) ° for x = 0.19 and 0.23, respectively. The general features of this

phase diagram are qualitatively well described by MFT [Eq. (5)], although quantitative agreement

is far from perfect. Previous DFT calculations have concluded that the AFM configuration

becomes more stable than the FM configurations for x > 0.2.32 This result agrees with the observed

NPD results, but places a higher bound on the critical x than MFT. We note that unlike previous

reports,12,13 no evidence for a disordered magnetic phase was found.

The overestimation of TC and TN in the calculated model, may partly be a result of the mean-

field approximation, which is known for giving overestimates for critical temperatures.33 The best-

18

fitted absolute values for the exchange constants are similar to values that were computed by

DFT;13,32 however direct comparison is difficult due to the simplifications introduced in the mean-

field model. The Fe-Mn and Mn-Mn couplings are found to be negative along the c axis, which is

also the shortest axis. This suggests that the magnetic interaction between the Fe and Mn atoms is

a direct exchange interaction, since this interaction is known to change sign from FM to AFM with

decreasing interatomic distance as described by the Bethe-Slater curve.34 This suggestion is

corroborated by the DFT calculations which have shown that the Mn-Mn exchange coefficients

are negative along the c axis but positive along the a axis. Since the latter is longer than the former

by only 0.02 Å, we can obtain an estimate on the critical Mn-Mn distance to be in the 2.89–2.92

Å range.

The anomalous variation of the LPs with T (Fig. 8) and x (Fig. 3) indicates a strong

magnetoelastic interaction. This variation in interatomic distances in turn influences the strength

of the exchange interaction between the magnetic M atoms, giving rise to a complicated

dependence of the ordered magnetic moment on T and x (Fig. 9). These subtleties were not

considered in our simplified model. In addition, the magnetoelastic interaction in these compounds

is highly anisotropic, as can be seen from the qualitatively different temperature evolution of the

LPs (Fig. 8). For x ≤ 0.5 the magnetic moment is highly affected by the c LP, causing an anomalous

expansion upon cooling. A similar dependence was observed in Mn2AlB2 for the b LP and

indicated a change in the anisotropy of the magnetoelastic interaction.21

The addition of Mn into Fe2AlB2 decreases the ordered FM moment, which in turn decreases

the overall magnetocaloric effect (Table II). However, the maximum in the magnetic entropy

change occurs over a broader temperature range [Fig. 6(b)] resulting in a 6% increase in the

estimated RCP (Table II). The addition of Mn does not seem to broaden the magnetic transition,

as can be observed from the temperature evolution of the ordered magnetic moments [Fig. 9(a)].

Additionally, since, as discussed above, the introduction of Mn does not produce multiple phases

in the sample but is admixed homogeneously, we can conclude that the broadening of the MCE

curve is not caused by chemical disorder but rather by the introduction of competing AFM

interactions, which are theoretically known to broaden the range of the MCE.17 Addition of 10%

Mn decreases TC from ≈290 K to ≈260 K while the effective temperature range or FWHM of the

MCE stays at ≈30 K. This enables control over TC in the RT range without a substantial loss of

cooling power. For example, mixing multiple (Fe1−xMnx)2AlB2 compounds with different x can

result in a combined MCE curve with a desired shape, which is controlled by the ratio of different

compounds and their respective TC’s.

VII. Conclusions

The magnetic phase diagram of the quaternary boride, (Fe1−xMnx)2AlB2, was studied using x-

ray- and neutron-powder diffraction, and magnetization measurements. In agreement with MFT

predictions, this system offers three magnetic ground states at different Mn concentrations:

ferromagnetic (FM), antiferromagnetic (AFM), and a canted AFM (Fig. 10).

19

While the addition of Mn decreases the critical temperature [Fig. 9(b)], FM moment (Fig. 10),

and magnetic entropy changes [Fig. 6(b)], it does increase the relative cooling power for Mn

additions up to x ≈ 0.2. This comes about due to the broadening of the temperature range, over

which the magnetocaloric effect is significant. It is therefore possible to fine tune the transition

temperature of Fe2AlB2 in the 274‒294 K (0–20 ℃) range without a considerable loss of cooling

power.

Acknowledgements

D.P. thanks E. Greenberg for help with performing XRD measurements. A.P, A.K, D.P,

O.R and E.N.C acknowledge the support of the Israel Atomic Energy Commission Pazy

Foundation Grant. H.A.E. thanks the National Research Council (USA) for financial support

through the Research Associate Program. S.K., M.S., L.H. and M.W.B. acknowledge the Knut and

Alice Wallenberg Foundation (Grant No. KAW 2015.0043).

Certain commercial equipment, instruments, or materials (or suppliers, or software, ...) are

identified in this paper to foster understanding. Such identification does not imply recommendation

or endorsement by the National Institute of Standards and Technology, nor does it imply that the

materials or equipment identified are necessarily the best available for the purpose.

References

1 V.K. Pecharsky and K.A. Gschneidner, Jr., Phys. Rev. Lett. 78, 4494 (1997).

2 V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, and A. Conde, Prog. Mater.

Sci. 93, 112 (2018).

3 O. Tegus, E. Brück, K.H.J. Buschow, and F.R. De Boer, Nature 415, 150 (2002).

4 X.F. Miao, L. Caron, P. Roy, N.H. Dung, L. Zhang, W.A. Kockelmann, R.A. De Groot, N.H.

Van Dijk, and E. Brück, Phys. Rev. B 89, 174429 (2014).

5 T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Manosa, and A. Planes, Nat.

Mater. 4, 450 (2005).

6 M. Ade and H. Hillebrecht, Inorg. Chem. 54, 6122 (2015).

7 S. Kota, M. Sokol, and M.W. Barsoum, Int. Mater. Rev. 65, 226 (2019).

8 J. Cedervall, M.S. Andersson, T. Sarkar, E.K. Delczeg-Czirjak, L. Bergqvist, T.C. Hansen, P.

Beran, P. Nordblad, and M. Sahlberg, J. Alloys Compd. 664, 784 (2016).

9 T.N. Lamichhane, K. Rana, Q. Lin, S.L. Bud’Ko, Y. Furukawa, and P.C. Canfield, Phys. Rev.

Mater. 3, 1 (2019).

10 S. Kota, W. Wang, J. Lu, V. Natu, C. Opagiste, G. Ying, L. Hultman, S.J. May, and M.W.

Barsoum, J. Alloys Compd. 767, 474 (2018).

20

11 P. Chai, S.A. Stoian, X. Tan, P.A. Dube, and M. Shatruk, J. Solid State Chem. 224, 52 (2015).

12 Q. Du, G. Chen, W. Yang, J. Wei, M. Hua, H. Du, C. Wang, S. Liu, J. Han, Y. Zhang, and J.

Yang, J. Phys. D. Appl. Phys. 48, 335001 (2015).

13 J. Cedervall, M.S. Andersson, D. Iuşan, E.K. Delczeg-Czirjak, U. Jansson, P. Nordblad, and M.

Sahlberg, J. Magn. Magn. Mater. 482, 54 (2019).

14 R. Barua, B.T. Lejeune, B.A. Jensen, L. Ke, R.W. McCallum, M.J. Kramer, and L.H. Lewis, J.

Alloys Compd. 777, 1030 (2019).

15 S. Hirt, F. Yuan, Y. Mozharivskyj, and H. Hillebrecht, Inorg. Chem. 55, 9677 (2016).

16 Z. Zhang, G. Yao, L. Zhang, P. Jia, X. Fu, W. Cui, and Q. Wang, J. Magn. Magn. Mater. 484,

154 (2019).

17 N.A. de Oliveira and P.J. von Ranke, Phys. Rep. 489, 89 (2010).

18 See Supplemental Material for sample preparation methods and additional XRD, magnetization

and NPD data.

19 B. Anasori, J. Lu, O. Rivin, M. Dahlqvist, J. Halim, C. Voigt, J. Rosen, L. Hultman, M.W.

Barsoum, and E.N. Caspi, Inorg. Chem. 58, 1100 (2019).

20 F. Matsubara and S. Inawashiro, J. Phys. Soc. Japan 46, 1740 (1979).

21 D. Potashnikov, E.N. Caspi, A. Pesach, A. Hoser, S. Kota, L. Verger, M.W. Barsoum, I. Felner,

A. Keren, and O. Rivin, J. Magn. Magn. Mater. 471, 468 (2019).

22 J.S. Smart, Effective Field Theories of Magnetism (Saunders Philadelphia & London, 1966).

23 D.G. Rancourt, M. Dubé, and P.R.L. Heron, J. Magn. Magn. Mater. 125, 39 (1993).

24 A.S. Cooper, Acta Crystallogr. 15, 578 (1962).

25 J.G. Barlock, and L.F. Mondolfo, Zeitschrift Fur Met. 66, 605 (1975).

26 J. Rodríguez-Carvajal, Phys. B Condens. Matter 192, 55 (1993).

27 L. Vegard, Zeitschrift Für Phys. 5, 17 (1921).

28 M. Földeàki, R. Chahine, and T.K. Bose, J. Appl. Phys. 77, 3528 (1995).

29 A. El Boukili, N. Tahiri, E. Salmani, H. Ez-Zahraouy, M. Hamedoun, A. Benyoussef, M. Balli,

and O. Mounkachi, Intermetallics 104, 84 (2019).

30 X. Tan, P. Chai, C.M. Thompson, and M. Shatruk, J. Am. Chem. Soc. 135, 9553 (2013).

31 Q. Du, G. Chen, W. Yang, Z. Song, M. Hua, H. Du, C. Wang, S. Liu, J. Han, Y. Zhang, and J.

Yang, Jpn. J. Appl. Phys. 54, 053003 (2015).

32 L. Ke, B.N. Harmon, and M.J. Kramer, Phys. Rev. B 95, 104427 (2017).

33 D.J. Singh and D.A. Papaconstantopoulos, Electronic Structure and Magnetism of Complex

Materials (Springer Science & Business Media, 2013).

21

34 A. Sommerfeld and H. Bethe, Hanbuch Der Physik (Springer, Berlin, 1933).

22

Supplemental Material

I. Sample preparation

All samples were prepared using a powder metallurgical route. Elemental Fe (Alfa Aesar,

99.5% metals basis, 6-10 µm, reduced), Mn (Alfa Aesar, 99.6% metals basis, < 10 µm), Al (Alfa

Aesar, 99.5% metals basis, < 44 µm), and 11B powders (Cambridge Isotopes, 99%) were used as

reagents. The as-received 11B was ground in an agate mortar and pestle, sieved to obtain a particle

size < 44 µm. The 11B powders were then washed in a 10 wt.% HF solution for 4 hours at room

temperature to remove SiO2 impurites, washed in distilled water, and dried in ambient air before

further processing. Some compositions were instead, or additionally, prepared using “natural” B

powders (Alfa Aesar, 98.8% metals basis, crystalline, <38 m) containing a natural abundance of 10B and 11B isotopes (denoted as NB for brevity). The methods used to prepare samples of a given

(Fe1-xMnx)2AlB2 solid solution composition are summarized in Table SIII. All reaction steps were

conducted in an atmosphere of flowing Ar (99.9999% purity) inside a horizontal alumina tube

furnace with both Ti and Y powders upstream as oxygen getters.

A. Method 1

First, Fe, Mn, and B were reacted to form (Fe1-xMnx)B ternary boride solid solutions and then

reacted with Al to make the quaternary (Fe1-xMnx)2AlB2 solid solutions. 4.5 grams of the elemental

powders were mixed in molar ratios of (1 − x)Fe + xMn + 1.025 11B, wherein x = (0, 0.05, 0.10

and 0.20). The mixtures were ball milled for 24 hours in plastic jars with an equal mass of yttria-

stabilized zirconia media. Green bodies were uniaxially cold pressed at 200 MPa into 2.5 cm wide

disks. All formulations were heated at a rate of 5 K/min in a horizontal tube furnace to 1474 K

(1200 ℃) and held at this temperature for 5 h before cooling at the same rate to room temperature.

The reacted (Fe1-xMnx)B ternary boride pellets were then crushed with an agate mortar and pestle

and sieved to a size < 44 µm. The ternary borides were mixed with Al in molar ratios of 2(Fe1-

xMnx)B + 1.2Al then ball milled and pressed into green bodies as described above. The pellets were

heated at a rate of 5 K/min to 1324 K (1050 ℃) and maintained at this temperature for 15 h before

cooling to room temperature. All samples were then ground and sieved to obtain particles < 44

µm.

B. Method 2

In this case, elemental powders in the molar ratio (2 − 2x)Fe + (2x)Mn + 1.2Al + 2 NB powders

were ball milled and cold-pressed into pellets as described above. The pellets were heated at a rate

of 5 K/min to 1324 K and maintained at this temperature for 1 h before cooling to room

temperature. The loosely sintered pellets were pulverized in an agate mortar and pestle, re-pressed

into a pellet, and re-heated again at 1324 K for 15 h. The reacted pellets were pulverized into

powders for further characterization and magnetic measurements.

23

Table SIII. Summary of compositions prepared and the corresponding synthesis method used.

Boron Reagent

Nominal x 11B NB

0 Method 1 Method 1

0.05 Method 1 N/A

0.1 Method 1 N/A

0.2 Method 1 N/A

0.25 Method 2 Method 2

0.3 Method 2 Method 2

0.5 Method 2a Method 2

0.75 Method 2 Method 2

1 Method 2a Method 2 a 11B reagent was not purified with HF treatment prior to reaction (i.e. used as-received)

24

FIG. S1. Observed XRD pattern (symbols) and the corresponding Rietveld refinement (solid line)

for a natural B (Fe0.5Mn0.5)2AlB2. Reflections are labeled by their Miller indices; impurity

reflections are marked by * for Al2O3 and # for (Fe1-yMny)4Al13. The measurement was performed

using a Bruker D8 – Advance. The error bars are smaller than the symbol size.

25

FIG. S2. Observed XRD pattern (symbols) and the corresponding Rietveld refinement (solid line)

for a natural B (Fe0.25Mn0.75)2AlB2. Reflections are labeled by their Miller indices; impurity

reflections are marked by * for Al2O3 and # for (Fe1-yMny)4Al13. The measurement was performed

using a Bruker D8 – Advance. The error bars are smaller than the symbol size.

26

FIG. S3. Arrott plots for (Fe1-xMnx)2AlB2 with x = 0 (a), 0.1 (b), 0.2 (c), 0.25 (d), and 0.3 (e). The

error bars are smaller than the symbol size. The temperature step in each sample is 5 K. Note: μ0

Oe = 10−4 Tesla and emu = 10−3 A m2.

27

28

FIG. S4. Observed NPD pattern of (Fe0.9Mn0.1)2AlB2 powders (symbols) at 298 K, the

corresponding Rietveld refinement (solid line), and their difference (solid blue line). Reflections

are labeled by their Miller indices; impurity reflections are marked by * for Al2O3 and “?” for

unidentified phases. Inset zooms in on the FM (001) reflection that appears below 260 K. The

measurement was performed using the BT-1 diffractometer. The error bars are smaller than the

symbol size.

29

FIG. S5. Observed NPD pattern of (Fe0.75Mn0.25)2AlB2 powders (symbols) at (a) 298 K, (b) 3 K,

the corresponding Rietveld refinement (solid line), and their difference (solid blue line).

Reflections are labeled by their Miller indices; impurity reflections are marked by * for Al2O3.

Inset in (a) zooms in on the FM (001) reflection, inset in (b) zooms in on the AFM (001/2)

reflection. The dashed green line shows the calculated profile at 298 K. The measurement was

performed using the KANDI-II diffractometer. The error bars are smaller than the symbol size.

30

FIG. S6. Observed NPD pattern of (Fe0.5Mn0.5)2AlB2 powders (symbols) at (a) 298 K, (b) 3 K, the

corresponding Rietveld refinement (solid line), and their difference (solid blue line). Reflections

are labeled by their Miller indices; impurity reflections are marked by # for (Fe1-yMny)4Al13 and ♦

for (Fe1-zMnz)B. Insets zooms in on the AFM (001/2) reflection. The measurement was performed

using the KANDI-II diffractometer. The error bars are smaller than the symbol size.

31

FIG. S7. Temperature evolution of the a and c LPs (left y axis) and b (right y axis) of (a)

(Fe0.9Mn0.1)2AlB2 and (b) (Fe0.8Mn0.2)2AlB2 determined from the NPD patterns.